Protesters have attacked banks and government buildings and burned a police motorcycle. Two protesters were shot dead in the western town of Dorud on Saturday night.

People protest in Tehran, Iran on December 30, 2017 in this picture obtained from social media. (REUTERS)

London: Protesters in Iran who have staged three days of demonstrations over economic hardship and alleged corruption should pay a high price if they break the law, the government said on Sunday.

The wave of anti-government demonstrations in several cities are the biggest challenge to Iran's leaders since unrest in 2009 that followed the disputed re-election of then-President Mahmoud Ahmadinejad went on for months.

Protesters have attacked banks and government buildings and burned a police motorcycle. Two protesters were shot dead in the western town of Dorud on Saturday night. The deputy governor of Lorestan province blamed foreign agents for the deaths.

"No shots were fired by the police and security forces. We have found evidence of enemies of the revolution, Takfiri groups and foreign agents in this clash," Habibollah Khojastehpour said in an interview on state television on Sunday. Takfiri is a term for Sunni militants, especially the Islamic State.

State media also quoted Interior Minister Abdolreza Rahmani Fazli as saying: "Those who damage public property, violate law and order and create unrest are responsible for their actions and should pay the price."

Ahmad Khatami, a hardline cleric who leads Friday prayers in the capital Tehran, said the protests were similar to those in 2009 over alleged electoral fraud.

He called for capital punishment for those chanting slogans against the values of the Islamic Republic.

The protests have included chants and slogans against Supreme Leader Ayatollah Ali Khamenei and the clerical leadership in power since 1979 revolution.

Videos posted on social media showed people chanting: "Mullahs, have some shame, let go of the country."

Protests defied the police and Revolutionary Guards who have used violence to crush previous unrest because they are motivated by economic grievances and have no clear leader.

They are also difficult for the government of President Hassan Rouhani because he was elected on a promise to guarantee rights to freedom of expression and assembly.

Rouhani's main achievement, a 2015 deal with world powers that curbed Iran's nuclear program in return for a lifting of most international sanctions, is yet to bring the economic benefits the government promised.

Unemployment rose to 12.4 percent this fiscal year up 1.4 percentage points, according to the Statistical Centre of Iran. 3.2 Iranians are jobless.